the graph shows the distribution of the length of videos (in seconds) on a popular video - sharing site. the…

the graph shows the distribution of the length of videos (in seconds) on a popular video - sharing site. the distribution is approximately normal, with a mean of 264 seconds and a standard deviation of 75 seconds. what percentage of videos have lengths that are between 114 and 414 seconds? 68% 75% 95% 99.7% video length -36 39 114 189 264 339 414 489 564 length (seconds)

the graph shows the distribution of the length of videos (in seconds) on a popular video - sharing site. the distribution is approximately normal, with a mean of 264 seconds and a standard deviation of 75 seconds. what percentage of videos have lengths that are between 114 and 414 seconds? 68% 75% 95% 99.7% video length -36 39 114 189 264 339 414 489 564 length (seconds)

Answer

Answer:

95%

Explanation:

Step1: Calculate z - scores

For (x = 114), (z_1=\frac{114 - 264}{75}=\frac{- 150}{75}=-2) For (x = 414), (z_2=\frac{414 - 264}{75}=\frac{150}{75}=2)

Step2: Use the empirical rule

The empirical rule for a normal - distribution states that approximately 95% of the data lies within (z=-2) and (z = 2) standard deviations of the mean. So the percentage of videos with lengths between 114 and 414 seconds is 95%.